CSCI-6962 Advanced Computer Graphics, Fall 2005
Assignment 1: OpenGL Warmup
The goal of this assignment is to get comfortable with the programming
environment you will be using for this class, familiarize yourself
with two simple libraries that we will use for linear algebra and
images, and learn how to submit assignments through WebCT. It's an opportunity for a
crash course in C++ and OpenGL (if you're not already familiar with
them). Here are a couple tutorials you may want to check out:
The incidental goal is also to have fun with bizarre fractal objects.
IFS are self-similar fractals: a subpart of the object is similar to
the whole. The classic example of an IFS is Barnsley's fern, where
each subpart of the fern is exactly the same as the whole fern. IFS
are described by a set of affine transformations (rotations,
translations, scale, skew, etc.) These transformations capture the
self-similarity of the object. IFS can be defined in any dimension,
and we will play with both two-dimensional and three-dimensional ones.
Formally, an IFS is defined by n affine transformations. Each
transformation fi must be contractive: The
distance between points must be reduced. An attractor of the
IFS is the object such that A = U fi (A).
A is unchanged by the set of transformations: It is a fixed
point.
We can render an IFS by iterating the transform on random input points
from the unit square. We approximate the fixed point by applying the
transformation many times. The algorithm is as follows:
for "lots" of random points (x0, y0)
for k=0 to num_iters
pick a random transform fi
(xk+1, yk+1) = fi(xk, yk)
display a dot at (xk, yk)
To reduce the number of points necessary to make an image of
reasonable quality, probabilities are assigned to each transformation,
instead of choosing a transformation with uniform probability.
Tasks
- Download the provided source code and compile it in your favorite
C++ environment. This should be where you plan to do all your
assignments for the course. A (optional) Makefile is provided for use
with either Linux or Windows(cygwin).
For interactive display of your IFS, you will use the OpenGL API that
uses graphics hardware for fast rendering of 3D primitives. Note: with
some configurations, software emulation might be used, resulting in
slower rendering. If the machine you're working on does not have
OpenGL and GLUT, you will need to download these libraries yourself
from http://www.opengl.org. All
files implementing OpenGL code should include the OpenGL header files:
// Included files for OpenGL Rendering
#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>
When provided with appropriate arguments, the initial executable
should launch an OpenGL window and draw a cube and you should be able
to navigate the scene with the mouse (left button rotates, middle
button translates, right button zooms). Try this at the command
prompt:
ifs -gui -size 500
- Now you're ready to start coding. Write a C++ class IFS
that renders iterated function systems, including the interface (in a
file ifs.h) and the implementation (ifs.C). The IFS
class should include:
- a field to store n, the number of transformations,
- an array of matrices representing the n transformations,
- an array of the corresponding probabilities for choosing a
transformation,
- a constructor that parses the input file and creates an IFS,
- a render method that creates and saves and image of the IFS,
- a paint method which makes appropriate OpenGL calls to draw points
or polygons to the OpenGL window, and
- a destructor that frees the memory of the various arrays (using
delete).
- When you're done, adjust the main function (provided in
main.C) if necessary so your program creates an
Image instance, reads an IFS description from a file, and
(depending on the command line arguments) either renders and saves
the IFS to the image or launches the OpenGL window as appropriate.
- Use the linear algebra library for the point and transformation
representations.
- Perform proper memory management --- free memory when an object
is destroyed. In many graphics applications careful management of
resources is essential!
- Comment on the performance of your programming environment. How
many polygons/points can you render interactively? What
improvements could you make to your code?
Ideas for Extra Credit
- create a new IFS, figure out the probabilities, etc.
- automatically determine the bounding box of the fractal object,
- change the color scheme,
- anti-aliasing,
- depth-first vs. breadth-first, etc.
Include a short paragraph in your README.txt file describing
your extensions.
Hints
- Random numbers can be obtained using the drand48() or
rand(), and RAND_MAX. See
stdlib.h.
- To debug your code, set the number of iterations to one. This
will allow you to check that you got the transformations right.
- Be careful, arrays are indexed from 0 to n-1 in
C++. Reading beyond the bounds of the array will probably result in a
segmentation fault.
- Use assert() to check function pre-conditions, array
indices, etc. See assert.h.
- To perform transformations in OpenGL, read about the Modelview
matrix stack and the OpenGL commands glMatrixMode(),
glPushMatrix(), glPopMatrix(), and
glMultMatrix().
Additional references
Image Library
The Image class is used to initialize and edit the rgb values
of images. Be careful --- do not try to edit values outside the
bounds of the image. The class also includes functions for loading
and saving simple .tga image files. .tga files can
be viewed with xv or opened in Photoshop and other Windows
image viewers/editors. The unix command line program mogrify
is useful for converting between different image representations.
Linear Algebra Library
Linear algebra support for floating point vectors with 2, 3, and 4
elements (Vec2f, Vec3f, and Vec4f) and 4x4
floating point matrices (Matrix). For this assignment, the
void Matrix::Transform(Vec3f &v) function will be handy.
Parsing code for command-line arguments and input files
Your program should take a number of command line arguments to specify
the input file (-input), number of points (-points),
number of iterations (-iters), output size (-size),
and whether to render to an output image file (-output), or
launch the OpenGL window (-gui). If the gui is selected,
draw points by default, or cubes if -cubes is specified.
Make sure the examples below work, as this is how we will test your
program. Code to parse input files and command line arguments is
provided:
OpenGL and main code
Makefile for g++ on LINUX or Windows (cygwin)
Data files
The input data for an IFS is a file which contains n,
the number of transforms, followed by the probability of choosing each
transform and a 4x4 floating point matrix representation of the
transform.
Sample Results
ifs -input sierpinski_triangle.txt -points 10000 -iters 0 -size 200 -output sierpinski_triangle_0.tga
ifs -input sierpinski_triangle.txt -points 10000 -iters 1 -size 200 -output sierpinski_triangle_1.tga
ifs -input sierpinski_triangle.txt -points 10000 -iters 2 -size 200 -output sierpinski_triangle_2.tga
ifs -input sierpinski_triangle.txt -points 10000 -iters 3 -size 200 -output sierpinski_triangle_3.tga
ifs -input sierpinski_triangle.txt -points 10000 -iters 4 -size 200 -output sierpinski_triangle_4.tga
ifs -input sierpinski_triangle.txt -points 10000 -iters 30 -size 200 -output sierpinski_triangle.tga
ifs -input fern.txt -points 50000 -iters 30 -size 400 -output fern.tga
ifs -input giant_x.txt -points 10000 -size 400 -gui -iters 0
ifs -input giant_x.txt -points 10000 -size 400 -gui -iters 1
ifs -input giant_x.txt -points 10000 -size 400 -gui -iters 2
ifs -input giant_x.txt -points 10000 -size 400 -gui -iters 3
ifs -input giant_x.txt -points 10000 -size 400 -gui -iters 4
ifs -input giant_x.txt -size 400 -gui -iters 0 -cubes
ifs -input giant_x.txt -size 400 -gui -iters 1 -cubes
ifs -input giant_x.txt -size 400 -gui -iters 2 -cubes
ifs -input giant_x.txt -size 400 -gui -iters 3 -cubes
ifs -input giant_x.txt -size 400 -gui -iters 4 -cubes
Please read the assignment information again before submitting.